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  <ul>
<li class="navelem"><b>cantor</b></li><li class="navelem"><a class="el" href="classcantor_1_1_cantor.html">Cantor</a></li>  </ul>
</div>
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<div class="header">
  <div class="summary">
<a href="#pub-static-methods">Static Public Member Functions</a> &#124;
<a href="classcantor_1_1_cantor-members.html">List of all members</a>  </div>
  <div class="headertitle">
<div class="title">cantor.Cantor Class Reference</div>  </div>
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<div class="contents">
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-static-methods"></a>
Static Public Member Functions</h2></td></tr>
<tr class="memitem:af054a78301a4cc06e172a7ed442381e7"><td class="memItemLeft" align="right" valign="top">def&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcantor_1_1_cantor.html#af054a78301a4cc06e172a7ed442381e7">pair</a></td></tr>
<tr class="memdesc:af054a78301a4cc06e172a7ed442381e7"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the <a class="el" href="classcantor_1_1_cantor.html">Cantor</a> pair of the two numbers k1, and k2.  <a href="#af054a78301a4cc06e172a7ed442381e7">More...</a><br/></td></tr>
<tr class="separator:af054a78301a4cc06e172a7ed442381e7"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a593ba595efb55ddc0b6d9b03e8165e3a"><td class="memItemLeft" align="right" valign="top">def&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcantor_1_1_cantor.html#a593ba595efb55ddc0b6d9b03e8165e3a">inv</a></td></tr>
<tr class="memdesc:a593ba595efb55ddc0b6d9b03e8165e3a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Separates a <a class="el" href="classcantor_1_1_cantor.html">Cantor</a> pair into two values k1, and k2.  <a href="#a593ba595efb55ddc0b6d9b03e8165e3a">More...</a><br/></td></tr>
<tr class="separator:a593ba595efb55ddc0b6d9b03e8165e3a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:adade70fac229147d138822b928282df3"><td class="memItemLeft" align="right" valign="top">def&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcantor_1_1_cantor.html#adade70fac229147d138822b928282df3">pairN</a></td></tr>
<tr class="separator:adade70fac229147d138822b928282df3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a357306f2bcee9ea4cb65e9546a7d3305"><td class="memItemLeft" align="right" valign="top">def&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcantor_1_1_cantor.html#a357306f2bcee9ea4cb65e9546a7d3305">invN</a></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>The <a class="el" href="classcantor_1_1_cantor.html">Cantor</a> pairing function is a pairing function. <a href="http://en.wikipedia.org/wiki/Cantor_pairing_function">http://en.wikipedia.org/wiki/Cantor_pairing_function</a> </p>
</div><h2 class="groupheader">Member Function Documentation</h2>
<a class="anchor" id="a593ba595efb55ddc0b6d9b03e8165e3a"></a>
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          <td class="memname">def cantor.Cantor.inv </td>
          <td>(</td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>z</em></td><td>)</td>
          <td></td>
        </tr>
      </table>
  </td>
  <td class="mlabels-right">
<span class="mlabels"><span class="mlabel">static</span></span>  </td>
  </tr>
</table>
</div><div class="memdoc">

<p>Separates a <a class="el" href="classcantor_1_1_cantor.html">Cantor</a> pair into two values k1, and k2. </p>
<p>Inverting the <a class="el" href="classcantor_1_1_cantor.html">Cantor</a> Pairing function requires the following 4 steps: <br/>
</p>
<ol type="1">
<li><img class="formulaInl" alt="$ w = \lfloor \frac{\sqrt{8z + 1} - 1}{2} \rfloor $" src="form_2.png"/> <br/>
</li>
<li><img class="formulaInl" alt="$ t = \frac{w^{2} + w}{2} $" src="form_3.png"/> <br/>
</li>
<li><img class="formulaInl" alt="$ y = z - t $" src="form_4.png"/> <br/>
</li>
<li><img class="formulaInl" alt="$ x = w - y $" src="form_5.png"/> <dl class="section pre"><dt>Precondition</dt><dd>none </dd></dl>
<dl class="section post"><dt>Postcondition</dt><dd>none </dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">z</td><td>A number assumed to be a <a class="el" href="classcantor_1_1_cantor.html">Cantor</a> pair. </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>Tuple of two numbers (k1, k2) that when <a class="el" href="classcantor_1_1_cantor.html">Cantor</a> paired produce the input parameter. </dd></dl>
</li>
</ol>

</div>
</div>
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          <td class="memname">def cantor.Cantor.invN </td>
          <td>(</td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>ps</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>n</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
  </td>
  <td class="mlabels-right">
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  </tr>
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</div><div class="memdoc">
<p>Separates a set of <a class="el" href="classcantor_1_1_cantor.html">Cantor</a> pairs into a set of elements. </p>
<dl class="section pre"><dt>Precondition</dt><dd>none </dd></dl>
<dl class="section post"><dt>Postcondition</dt><dd>none </dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">ps</td><td>A single number representing multiple <a class="el" href="classcantor_1_1_cantor.html">Cantor</a> pairs. </td></tr>
    <tr><td class="paramname">n</td><td>The number of pairs that ps is made of, and therefore should be split into. </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>A set of numbers representing the original set of numbers. </dd></dl>

</div>
</div>
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          <td class="memname">def cantor.Cantor.pair </td>
          <td>(</td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>k1</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>k2</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
  </td>
  <td class="mlabels-right">
<span class="mlabels"><span class="mlabel">static</span></span>  </td>
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<p>Returns the <a class="el" href="classcantor_1_1_cantor.html">Cantor</a> pair of the two numbers k1, and k2. </p>
<p>The <a class="el" href="classcantor_1_1_cantor.html">Cantor</a> Pairing function is defined as: <br/>
 <img class="formulaInl" alt="$ \pi(k_{1}, k_{2}) := \frac{1}{2}(k_{1} + k_{2})(k_{1} + k_{2} + 1) + k_{2} $" src="form_1.png"/> </p>
<dl class="section pre"><dt>Precondition</dt><dd>none </dd></dl>
<dl class="section post"><dt>Postcondition</dt><dd>none </dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">k1</td><td>A number in the range 0 to X. </td></tr>
    <tr><td class="paramname">k2</td><td>A number in the range 0 to Y. </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>The <a class="el" href="classcantor_1_1_cantor.html">Cantor</a> pairing of k1 and k2. </dd></dl>

</div>
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          <td class="memname">def cantor.Cantor.pairN </td>
          <td>(</td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>set</em></td><td>)</td>
          <td></td>
        </tr>
      </table>
  </td>
  <td class="mlabels-right">
<span class="mlabels"><span class="mlabel">static</span></span>  </td>
  </tr>
</table>
</div><div class="memdoc">
<p>Performs the <a class="el" href="classcantor_1_1_cantor.html">Cantor</a> pairing function over a set of elements. </p>
<dl class="section pre"><dt>Precondition</dt><dd>none </dd></dl>
<dl class="section post"><dt>Postcondition</dt><dd>none </dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">set</td><td>A list of elements to pair into a single number. </td></tr>
  </table>
  </dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>A number representing the paired numbers. </dd></dl>

</div>
</div>
<hr/>The documentation for this class was generated from the following file:<ul>
<li>rlblackjack/<a class="el" href="cantor_8py.html">cantor.py</a></li>
</ul>
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